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Manipal MET2018MathematicsDifferentiation

Derivative of x^x is

Options

  1. Ax^x(1- x)
  2. B1+ x
  3. Cx^x(1+ x)
  4. D1- x

Correct answer

C. x^x(1+ x)

Step-by-step solution

Let y=x^x Taking log on both sides, we get y=x x On differentiating w.r.t. x , we get aligned 1 y d y d x & = x x + x d y d x & =y(1+ x)=x^x(1+ x) aligned

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